Carlos Castro Perelman, Fang Fang, Klee Irwin (2013)

Inspired by the Sum of the Squares law obtained in the paper titled  The Sum of Squares Law  by J. Kovacs, F. Fang, G. Sadler and K. Irwin, we derive the law of the sums of the squares of the areas, volumes and hyper-volumes associated with the faces, cells and hyper-cells of regular polytopes in diverse dimensions after using Clifford algebraic methods.